mid-15c., "action of flowing," from flow (v.). Meaning "amount that flows" is from 1807. Sense of "any strong, progressive movement comparable to the flow of a river" is from 1640s. Flow chart attested from 1920 (flow-sheet in same sense from 1912). To go with the flow is by 1977, apparently originally in skiing jargon.

Go with the flow, enjoy the forces, let ankles, knees, hips and waist move subtly to soak up potential disturbances of acceleration and deceleration. ["Ski" magazine, November 1980]